1.. _msd: 2 3Mean Square Displacement 4------------------------ 5 6| :ref:`gmx msd <gmx msd>` 7| To determine the self diffusion 8 coefficient :math:`D_A` of 9 particles of type :math:`A`, one can use the Einstein 10 relation :ref:`108 <refAllen87>`: 11 12 .. math:: \lim_{t \rightarrow \infty} \langle 13 \|{\bf r}_i(t) - {\bf r}_i(0)\|^2 \rangle_{i \in A} ~=~ 6 D_A t 14 :label: eqnmsd 15 16| This *mean square displacement* and :math:`D_A` are calculated by the 17 program :ref:`gmx msd <gmx msd>`. Normally 18 an index file containing atom numbers is used and the MSD is averaged 19 over these atoms. For molecules consisting of more than one atom, 20 :math:`{\bf r}_i` can be taken as the center of mass positions of the 21 molecules. In that case, you should use an index file with molecule 22 numbers. The results will be nearly identical to averaging over atoms, 23 however. The :ref:`gmx msd <gmx msd>` program can also be used for 24 calculating diffusion in one or two dimensions. This is useful for 25 studying lateral diffusion on interfaces. 26 27An example of the mean square displacement of SPC water is given in 28:numref:`Fig. %s <fig-msdwater>`. 29 30.. _fig-msdwater: 31 32.. figure:: plots/msdwater.* 33 :width: 8.00000cm 34 35 Mean Square Displacement of SPC-water. 36 37 38